Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x \cdot 2 + y\right) + x \cdot x\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
y \cdot \left(x \cdot 2 + y\right) + x \cdot x
double f(double x, double y) {
        double r441756 = x;
        double r441757 = r441756 * r441756;
        double r441758 = 2.0;
        double r441759 = r441756 * r441758;
        double r441760 = y;
        double r441761 = r441759 * r441760;
        double r441762 = r441757 + r441761;
        double r441763 = r441760 * r441760;
        double r441764 = r441762 + r441763;
        return r441764;
}
↓
double f(double x, double y) {
        double r441765 = y;
        double r441766 = x;
        double r441767 = 2.0;
        double r441768 = r441766 * r441767;
        double r441769 = r441768 + r441765;
        double r441770 = r441765 * r441769;
        double r441771 = r441766 * r441766;
        double r441772 = r441770 + r441771;
        return r441772;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot x + \left(y \cdot y + \left(x \cdot y\right) \cdot 2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x \cdot 2 + y\right) + x \cdot x}\]

  3. Final simplification0.0

    \[\leadsto y \cdot \left(x \cdot 2 + y\right) + x \cdot x\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2)))

  (+ (+ (* x x) (* (* x 2) y)) (* y y)))